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20 May 2018, 14:22
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
57% (01:29) correct
43%
(01:19)
wrong
based on 526
sessions
History
Date
Time
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Not Attempted Yet
If x ≠ 0, what is the value of x ?
(1) \(|x^x| = 1\)
(2) \(x^5 = x^x\)
M36-134
(1) \(|x^x| = 1\)
(2) \(x^5 = x^x\)
M36-134
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17 Nov 2021, 02:31
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Bunuel
Official Solution:
If \(x ≠ 0\), what is the value of \(x\) ?
(1) \(|x^x| = 1\)
If \(x^x = 1\), then \(x=1\).
If \(x^x = -1\), then \(x=-1\).
Not sufficient.
(2) \(x^5 = x^x\)
Obviously \(x=1\) (\(1^5=1^1\)) and \(x=5\) (\(5^5=5^5\)) work. Since 5 is an odd exponent, let's check whether \(x=-1\) work: \((-1)^5=(-1)^{(-1)}\). It does. So, from this statement \(x=1\), \(x=5\) or \(x=-1\).
Not sufficient.
(1)+(2) \(x\) still can be 1 or -1. Not sufficient.
Answer: E
General Discussion
20 May 2018, 14:57
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Bunuel
We'll try finding numbers which give contradictory answers.
This is an Alternative approach.
(1) So x^x must equal 1 or -1. This can happen if the exponent is 0 which is impossible by question definition or if x = 1 or if x = -1.
That is, 1^1 = 1 and -1^-1 = -1 so in absolute value both equal 1.
Insufficient.
(2) If we're not sure where to start we'll try easy numbers. If x = 1 then 1^5 = 1^1 = 1 so x = 1 works. If x = 2 then 2^5 = 32 but 2^2 = 4 so x = 2 doesn't work. Since the exponent on the left is 5 it makes sense to try x = 5 which gives 5^5 = 5^5. So x = 1 and x = 5 both work.
Insufficient.
Combined:
x = 1 fits both criteria as shown above. How about x = -1? -1^5 = -1 and -1^-1 = -1. So both x = 1 and x = -1 fit both criteria.
Insufficient.
(E) is our answer.
